A qualitative study of flow regimes as a function of the sweep X, the Mach number Mo., and the angle of attack ~ under supersonic flow over delta wings with a sharp leading edge was carried out experimentally in [1, 2]. The effect of the angle of attack on the turbulent-laminar transition was studied in [3, 4]. It was shown that the transition for triangular plates with X = 60-75 ~ accelerates for c~ < 10 ~ and is delayed for r > 15 ~ In [5] the Stanton numbers were measured on the upwind side of delta wings for X = 65, 70 ~ ~x = 0-15 ~ M~. = 6.1 and 8. The results of the calculations of laminar and turbulent boundary layers on a flat delta wing are given in [6].Using the algorithm from [7, 8], below we carry out calculations for the compressed turbulent boundary layer on the upwind side of flat and profiled delta wings for M~, > 1. The parameters of the laminar-turbulent transition were chosen from a comparison of the distribution of the Stanton numbers with the experimental results [5]. We also study the effect that the determining parameters of the problem have on the distribution of local and overall surface friction coefficients.1. We consider the turbulent boundary layer on a profiled delta wing, whose leading edge has a sweep X. Its surface y = G(x, z) is given in Cartesian coordinates x, y, z with origin at the nose of the wing. The plane z = 0 coincides with its symmetry plane. The leading and trailing edges of the wing lie in the plane y = 0; z = f(x) is the equation of the leading edge. The velocity vector of the mainstream lies in the vertical symmetry plane of the wing and makes an angle of attack c~ with the x axis.To describe the boundary layer we introduce a nonorthogonal system of coordinates (~, 71, ~'), bound to the surface of the body:Here the coordinate ~" is reckoned from the leading edge in the section ~ = const; ~/ is the normal to the surface. The components u, v, w correspond to the coordinates ~, ~/, ~'. The complete equations of the compressed boundary layer in the variables ~, X, ~', where k = 7//~~-and the boundary conditions for the region 9 (~ >__ ~o, 0 < ~" < ~'~, 0 ~ X < Xe(~, ~')) are written out in [7, 8].The section ~ = ~o is given at the conical nose of the body and the profiles u o, Wo, T O are taken from the self-similar solution for the nose. At the leading edge (~" --0) the profiles u~, w~, T~ are determined from the solution of the ordinary differential equations obtained from the complete equations of the boundary layer by the passage to the limit ~" --, 0 on the assumption that all the sought functions and their derivatives are bounded. The usual attachment conditions for a viscous fluid and given at the surface of the body (X = 0) and the gas and the wall are assumed to be at the same temperature T = T w. At the outer boundary (k = ~(~, ~)) the parameters of the boundary layer are taken from calculations of the flow of nonviscous gas over the wing. The results given below were calculated for X = 70* by taking the data obtained by the method of [9] and those for X = 45...
